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Exotic open $4$–manifolds which are nonleaves

Carlos Meniño Cotón and Paul A Schweitzer

Geometry & Topology 22 (2018) 2791–2816
Abstract

We study the possibility of realizing exotic smooth structures on finitely punctured simply connected closed 4–manifolds as leaves of a codimension-one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open 4–manifolds which are not diffeomorphic to any leaf of a codimension-one C2 foliation on a compact manifold. These examples include some exotic 4 ’s and exotic cylinders S3 × .

Keywords
exotic $\mathbb{R}^4$, nonleaves, codimension-one foliations
Mathematical Subject Classification 2010
Primary: 37C85, 53C12, 57R30
Secondary: 57R55
References
Publication
Received: 25 November 2016
Revised: 13 November 2017
Accepted: 25 February 2018
Published: 1 June 2018
Proposed: Yasha Eliashberg
Seconded: András I Stipsicz, Leonid Polterovich
Authors
Carlos Meniño Cotón
Departamento de Análise, Instituto de Matemática e Estatística
Universidade Federal Fluminense
Niterói
Rio de Janeiro-RJ
Brazil
Paul A Schweitzer
Departamento de Matemática
Pontificia Universidade Católica do Rio de Janeiro
Gávea
Rio de Janeiro-RJ
Brazil